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The question is about emergence and reductionism.

Except for a few exceptions, such as dark matter, most phenomena in Nature could be reproduced from the standard model and general relativity with great accuracy. Up to a Planck scale, there is no inconsistency between general relativity and quantum theory by means of effective theory. However, at different level of complexity, a new principle may emerge. One example is the theory of evolution in Biology.

Is there any similar emerged master theory in Chemistry that comparable with evolution in Biology?

Here, the emerged master theory means:

  1. It is not just a brute-force ab initio computation (emergence). Here I have excluded explicitly correlated Gaussian.

  2. The theory is universally valid. Not like 8- and/or 18-electron principle and/or VSEPR and/or periodic table, we know there are many exceptions.

  3. The theory should generate experimentally testable predictions, hopefully quantitative. Here I have excluded Bader's QTAIM at its current form. Atom in molecule and types of chemical bonds are anyway not observables. One may see some correlation between Laplacian at bond critical point with other molecular properties, and do some fitting or hand-waving argument. Such fitted relation could be useful. However, it is a fitting, not a derivation from its principle. I do not regard it as a prediction.

  4. The theory should not be discovered in condensed matter physics first. Here I have excluded spontaneous symmetry breaking.

  5. I do not expect the statement like, there is no master principle in chemistry is the master principle in chemistry.

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    $\begingroup$ Chemistry is an extension of physics. Seeing as how you have excluded theory that is so rigorously defined as to allow quantitative computation, and also ignored the fact that Bader's QTAIM is derived from Schwinger's fundamental representation of quantum mechanics, I really don't see what is left to form a master theory. At least you discarded the octet rule, and hopefully also hypervalency and d-orbital participation. $\endgroup$ – Eric Brown Jun 2 '14 at 6:36
  • $\begingroup$ QTAIM is concerned, among many things, with the topological characteristics of the electron density, especially those that involve energy-lowering (bonding!) interactions between atoms (things that can be identifiable because they have the same boundary conditions that are consistent with QM, and one can practically execute this identification). The best place to see it in action is in crystallography, where x-ray diffraction can actually see the electron density to high enough resolution to identify things like critical points. $\endgroup$ – Eric Brown Jun 2 '14 at 6:50
  • $\begingroup$ what are you trying to do, divine the future? If you have a question, evaluate system A (predict its properties), then evaluate system B (predict its properties), and then you have A-B (the predicted change). Whether A or B have actually been observed is pretty much immaterial, due to the predictive power of quantum mechanics. $\endgroup$ – Eric Brown Jun 2 '14 at 6:54
  • $\begingroup$ But what are you trying to predict? Prediction of a chemical product/mechanism due to conservation of state symmetry? Well no doubt. Recall that the MO picture is formed once the state symmetry is already known. Hardly a prediction. Also, I can write many wrong (though valid!) qualitative MO pictures, the right one is found through observation and/or computation. How is this a prediction? $\endgroup$ – Eric Brown Jun 2 '14 at 7:07
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    $\begingroup$ @EricBrown It would be great if you could ask a self-answered question to capture some of this discussion, if the OP is not interested in doing so. $\endgroup$ – jonsca Jun 3 '14 at 23:05
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You may be asking for something quite a bit deeper, and it's rather hard to strictly adhere to the requirements in the question, but after Eric's interesting edit showing some outside-the-box thinking, I went along those lines and came up with some options. I'll let you decide which (if any) make the cut.

Two good candidates for master principles in chemistry may be acid-base theory and reduction-oxidation theory. I think ultimately they're just somewhat coarse measures of the relative positions between HOMOs and LUMOs for different species, but after a couple centuries of research and some tabulation, we've come up with general top-level rules for understanding the chemical behaviour of large classes of compounds, with significant predictive power, without necessarily resorting to complicated calculations.

The periodic table itself could also work; different elements possess certain chemical similarities which allows them to be grouped with one another. Mendeleev famously used this to predict a handful of new elements, such as germanium (though he did also predict some other elements which never came to be). A related principle which is simple but of great importance is that elements are entirely characterized by the number of protons in their nuclei. Every single atom in the Universe with 79 protons in its nucleus is a gold atom, no matter how many neutrons and electrons are present.

Also, I wonder if you'd count materialism as a master principle which emerged in chemistry; every material in the Universe is made of atoms (not counting dark matter). If two materials are the same, then they must be made of the same types and proportions of atoms in the same configurations. If two materials are different, then either the atoms are different, or they are present in different proportions, or they are present in different configurations.

Finally, I myself would actually have included the octet rule as a master principle. It has many holes and limited applicability, but it is uncanny that such a simple concept works at all. I find it a surprising way to effectively skip tons of gritty quantum mechanical calculations, helping chemistry education to begin in school around ages 14-15.

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Quantum Mechanics and Statistical Mechanics are the "master theories" of chemistry. Prediction can be had from difference of descriptions determined from these rigorously defined and realizable scientific concepts.

Relativistic contributions can be seen especially in heavier elements.

Edit: In the spirit of your question, perhaps you are looking for something that has evolved from chemistry, that may not have been directly apparent in the physics community. I would propose that the concept of a functional group--a rather predictably-behaving collection of atoms--is a master principle.

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  • $\begingroup$ The scope of chemistry is beyond Quantum Mechanics and Statistical Mechanics, so they cannot be the "master theories" of chemistry. To get a proper foundation for Chemistry it is needed to generalize both Quantum Mechanics and Statistical Mechanics. doi.org/10.1111/j.1749-6632.2003.tb06091.x $\endgroup$ – juanrga Sep 25 '18 at 17:17
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My question is, is there any similar emerged master theory in Chemistry that comparable with evolution in Biology?

I would answer classical electrostatics. Sure, you definitely can't use electrostatics to rationalize all of chemistry, but you can use it to a great extent in early and introductory chemistry.

Think about organic chemistry. The organizing principle of introductory organic chemistry is "nucleophile attacks electrophile." This will help you correctly draw most of the arrows you need to draw in organic chemistry.

There are a few classes of reactions that sort of fall out of this "motif," however:

Exceptions to motif: nucleophile attacks electrophile

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Main topic of chemistry is transformation of substances. Theory describing the transformation is the Transition state theory. It allows us to discern favourable processes from less favourable, show how the speed of reaction changes with temperature.

Once spiced with more advanced concepts, like Free energy relationship, it allows us to predict how the reactivity will change upon substitution.

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